Change this file (plugins/payment/offline/offline.html) 
to meet your needs for offline payment.

Payment#/Username: {$payment.payment_id}/{$member.login}
Price:     {$price}

Place instructions here for customers how to do payment.
Make sure customer will include username(login) and payment#
to payment description. Then it will be easy for you to find 
order later.

When you receive completed payment, check payment as "Completed"
in aMember control panel. User will receive email with login info
and will be able to enter into site.